Hybrid View

Basic Question About Matrix Stack

Suppose this is the Display function for a very simple OpenGL, GLUT, program.
How many matrices would this put on the matrix stack?
I used to think it would be 4. However, now I'm leaning towards 1,
which would be the product of the (Identity matrix) x (the Translation Matrix) x
(the Rotation matrix) x (the Scale Matrix).

Yeah, there's just 1 matrix manipulated by that code. All the transformation functions affect the matrix at the current stack depth. Matrices aren't put onto the stack unless you call glPushMatrix (duplicates current matrix + increases stack depth) + removed when you call glPopMatrix (reduces stack depth).
OpenGL only guarantees that GL_MODELVIEW will have a stack >=32 matrices, GL_TEXTURE has depth >=2, GL_COLOR has depth >=2, GL_MODELVIEW has depth >=2, so you shouldn't call glPushMatrix too many times without glPopMatrix calls.

BTW, mathematically that translates to MModelview = MI* MT* MR* MS so as you can see, the current matrix is computed by matrix commands concatenated in reverse order, with the first(right-most) matrix being specified by the last command and the last(left-most) matrix being specified by the first command.